First, we used a predator dataset to check whether we need to consider phylogeney. If so, we will use predator and prey datasets for following meta-analysis.
Study_ID Cohort_ID Shared_control_ID Year
Brilot_2009 :40 Jones_1980_1 :16 Jones_1980_a :16 Min. :1957
Jones_1980 :16 Brilot_2009_1:10 Brilot_2009_a:10 1st Qu.:2009
Vallin_2011 :10 Brilot_2009_2:10 Brilot_2009_b:10 Median :2009
Hossie_2015 : 8 Brilot_2009_3:10 Brilot_2009_c:10 Mean :2005
Olofsson_2015: 7 Brilot_2009_4:10 Brilot_2009_d:10 3rd Qu.:2013
Vallin_2010 : 5 Vallin_2011_1:10 Vallin_2011_a:10 Max. :2016
(Other) :31 (Other) :51 (Other) :51
Country Data_source Data_location Bird_species
Canada : 8 table. 1 :21 p.187 :24 Cyanocitta_cristata: 2
Finland:14 fig. 3 :15 p.186 :16 Emberiza_sulphurata: 1
India : 2 fig. 2 :12 p.214 :16 Ficedula_hypoleuca : 2
Sweden :24 text, fig. 3:10 p.1663 :10 Gallus_gallus :48
UK :67 text : 9 p.13 : 5 Parus_caeruleus :19
US : 2 fig. 4a : 8 p.1419 : 4 Parus_major : 3
(Other) :42 (Other):42 Sturnus_vulgaris :42
Bird_common_name Prey_species
blue jay : 2 Caligo_martia : 2
blue tit :19 Inachis_io : 6
common starling:42 Junonia_almana : 3
domestic fowl :48 Lasiommata_megera:11
great tit : 3 none :88
pied flycatcher: 2 Pieris_rapae : 2
yellow bunting : 1 Saturnia_pavonia : 5
Prey_common_name Response Measure
emperor moth : 5 continuous :75 latency :61
European cabbage butterfly: 2 proportion1:16 number :15
none :88 proportion2:26 proportion:39
owl butterfly : 2 time : 2
peacock butterfly : 6
peacock pansy butterfly : 3
wall brown butterfly :11
Direction Detail_result
Decrease:24 latency to attack :10
Increase:81 proportion of time spent near eyespot : 9
Neutral :12 latency to approach the food bowl : 8
latency to first movement : 8
propotion of time spent furthest from eyespot: 8
proportion of time spent on foodbowl : 7
(Other) :67
Note_result
:107
including wing flaps and/or jumping : 1
mean time in seconds from the beginning of a trial to when a blue tit first visited the log on the floor (first visit): 3
the time from landing on the perch in front of the butterfly until the attack was launched : 4
total number of day 1 to 5, reversed value : 1
weak and intense alarm call : 1
Treatment_stimulus Number_pattern Diameter_pattern Area_pattern
conspicuous: 7 Min. :1.00 Min. : 2.20 Min. : 3.801
eyespot :110 1st Qu.:1.00 1st Qu.: 4.50 1st Qu.: 15.904
Median :2.00 Median :20.00 Median : 87.715
Mean :1.94 Mean :15.29 Mean :254.622
3rd Qu.:2.00 3rd Qu.:25.00 3rd Qu.:489.697
Max. :5.00 Max. :31.28 Max. :490.874
Area_background Shape_pattern Control_stimulus
Min. : 225 circle : 6 camouflage: 10
1st Qu.: 1000 eyespot:110 no pattern:107
Median : 3200 stripe : 1
Mean : 5851
3rd Qu.:13175
Max. :26400
Note_stimulus
:22
single wing; painted over eyespot on about half of the butterflies (ヤeyespot painted overユ) and sham-painted an equally large area just beside the eyespot on the rest of the butterflies (ヤeyespot visibleユ): 6
ambiguous eyespot; based on a photographof owl eyes with a contrasting light iris and dark pupil; with alarm call : 5
ambiguous eyespot; based on a photographof owl eyes with a contrasting light iris and dark pupil; with sparrowhawk call : 5
ambiguous eyespot; based on a photographof owl eyes with a contrasting light iris and dark pupil; with threat call : 5
ambiguous eyespot; based on a photographof owl eyes with a contrasting light iris and dark pupil; with white noise : 5
(Other) :69
Type_prey Shape_prey Diet_bird Bird_sex
artificial:88 abstract_butterfly :14 grainivore : 1 both :50
real :29 abstract_caterpillar:16 Invertebrate: 2 female:12
abstract_prey :58 omnivore :114 male :16
butterfly :29 NA's :39
Bird_age Tn Cn T_mean
adult :48 Min. : 4.00 Min. : 4.00 Min. : 0.0004
chick :38 1st Qu.: 8.00 1st Qu.: 8.00 1st Qu.: 0.7656
juvenile: 4 Median : 9.00 Median : 9.00 Median : 16.1000
NA's :27 Mean :14.73 Mean :14.26 Mean : 119.1540
3rd Qu.:15.00 3rd Qu.:15.00 3rd Qu.: 153.5000
Max. :89.00 Max. :89.00 Max. :1180.4878
NA's :16
C_mean MT_mean MC_mean
Min. : 0.0400 Min. :-556.1000 Min. :-2115.0000
1st Qu.: 0.5079 1st Qu.: -6.8415 1st Qu.: -13.6000
Median : 9.3000 Median : 0.7544 Median : 0.5543
Mean : 110.1728 Mean : -43.7981 Mean : -121.8786
3rd Qu.: 154.2000 3rd Qu.: 0.9522 3rd Qu.: 0.9174
Max. :2115.0000 Max. : 0.9996 Max. : 0.9574
NA's :16 NA's :81 NA's :81
T_sd C_sd T_proportion C_proportion
Min. : 0.0100 Min. : 0.0500 Min. :0.01000 Min. :0.04262
1st Qu.: 0.5183 1st Qu.: 0.2859 1st Qu.:0.05258 1st Qu.:0.08262
Median : 16.9814 Median : 4.7434 Median :0.27152 Median :0.26477
Mean : 82.2725 Mean : 78.2657 Mean :0.30879 Mean :0.29854
3rd Qu.: 74.7486 3rd Qu.: 56.2141 3rd Qu.:0.49500 3rd Qu.:0.50000
Max. :731.8482 Max. :1052.1749 Max. :0.82609 Max. :0.79618
NA's :16 NA's :16 NA's :75 NA's :75
Study_design Dataset Mean_median T_mean_median
dependent :64 predator:117 mea : 1 Min. : 0.0004
independent:53 mean :99 1st Qu.: 0.7656
median: 1 Median : 12.0000
NA's :16 Mean : 104.2470
3rd Qu.: 104.0000
Max. :1180.4878
C_mean_median Type_of_variance_statistic T_se
Min. : 0.0000 IQR : 1 Min. : 0.00000
1st Qu.: 0.6559 SD : 3 1st Qu.: 0.09462
Median : 9.3000 SE :28 Median : 4.88000
Mean : 96.8310 SE : 1 Mean : 25.83973
3rd Qu.: 61.0000 SEM :68 3rd Qu.: 24.68328
Max. :2115.0000 NA's:16 Max. :182.92683
NA's :20
C_se T_variance_q1 T_variance_q3 C_variance_q1 C_variance_q3
Min. : 0.0000 Min. :77.5 Min. :246 Min. :29 Min. :36
1st Qu.: 0.0903 1st Qu.:77.5 1st Qu.:246 1st Qu.:29 1st Qu.:36
Median : 1.5000 Median :77.5 Median :246 Median :29 Median :36
Mean : 26.7360 Mean :77.5 Mean :246 Mean :29 Mean :36
3rd Qu.: 19.8747 3rd Qu.:77.5 3rd Qu.:246 3rd Qu.:29 3rd Qu.:36
Max. :372.0000 Max. :77.5 Max. :246 Max. :29 Max. :36
NA's :20 NA's :116 NA's :116 NA's :116 NA's :116
Note
:72
authors only reported total sample size (left eyespots and right eyespots), so the sample size was equally divided between the two stimuli: 8
Mann-Whitney U test; p < 0.002 : 4
ア 1 SEM : 4
Calculated by AM : 3
(Other) :24
NA's : 2
lnRR lnRR_var Obs_ID Log_diameter
Min. :-2.15769 Min. :0.0008295 Min. : 1 Min. :0.7885
1st Qu.:-0.07696 1st Qu.:0.0107871 1st Qu.: 30 1st Qu.:1.5041
Median : 0.08779 Median :0.0333636 Median : 59 Median :2.9957
Mean : 0.27498 Mean :0.1249595 Mean : 59 Mean :2.4180
3rd Qu.: 0.54880 3rd Qu.:0.1655345 3rd Qu.: 88 3rd Qu.:3.2189
Max. : 4.16777 Max. :1.3885984 Max. :117 Max. :3.4430
Log_area Log_background
Min. :1.335 Min. : 5.416
1st Qu.:2.767 1st Qu.: 6.908
Median :4.474 Median : 8.071
Mean :4.574 Mean : 7.819
3rd Qu.:6.194 3rd Qu.: 9.486
Max. :6.196 Max. :10.181
Code
summary(dt_prey)
Study_ID Cohort_ID Shared_control_ID
Hossie_2013 :25 Hossie_2013_13 : 13 Hossie_2013_g : 13
Hossie_2012 :24 Hossie_2012_19 : 6 Stevens_2007_b : 8
Stevens_2007 :20 Ho_2016_13 : 2 deWert_2012_a : 7
Ho_2016 :18 Ho_2016_14 : 2 Hossie_2012_j : 6
Stevens&Hardman_2008:14 Ho_2016_15 : 2 Stevens_2007_d : 6
Stevens&Cantor_2009 :12 Vallin_2010_2_1: 2 Stevens&Cantor_2009_a: 6
(Other) :40 (Other) :126 (Other) :107
Year Country Data_source Data_location
Min. :2003 Canada :49 fig. 4 :32 supplementary Material:54
1st Qu.:2008 Finland : 2 fig. S2 :30 p.387 :12
Median :2012 Germany : 2 fig. 3 :18 p.1223 :10
Mean :2011 Singapore:18 table. S1:18 p.529 : 9
3rd Qu.:2013 Sweden : 8 fig. 5 : 8 p.1222 : 8
Max. :2022 UK :71 fig. 7 : 8 p.27 : 7
US : 3 (Other) :39 (Other) :53
Bird_species Bird_common_name Prey_species
Ficedula_hypoleuca: 2 blue tit : 8 Bicyclus_anynana : 2
none :143 none :143 Inachis_io : 2
Parus_caeruleus : 8 pied flycatcher: 2 Mycalesis_perseus: 18
none :116
Saturnia_pavonia : 8
Thyatira batis : 7
Prey_common_name Response Measure
Bicyclus anynana : 2 continuous : 19 number : 19
dingy bush brown butterfly: 18 proportion1:131 proportion:134
emperor moth : 8 proportion2: 3
none :116
peacock butterfly : 2
Thyatira batis : 7
Direction Detail_result
Decrease: 6 attacked : 6
Increase:128 escaped : 1
Neutral : 19 number of attacked: 19
survival :127
Note_result Treatment_stimulus
:124 conspicuous:77
2 cm length : 1 eyespot :76
4 cm length : 1
6 cm length : 1
AM culculated the survival rate from raw data: 2
calculated by AM; (total-predated)/total : 24
Number_pattern Diameter_pattern Area_pattern Area_background
Min. : 1.000 Min. : 1.700 Min. : 2.27 Min. : 129.6
1st Qu.: 2.000 1st Qu.: 4.500 1st Qu.: 15.90 1st Qu.: 625.0
Median : 2.000 Median : 6.000 Median : 28.27 Median : 913.9
Mean : 2.562 Mean : 6.759 Mean : 35.30 Mean : 891.2
3rd Qu.: 2.000 3rd Qu.: 8.380 3rd Qu.: 43.01 3rd Qu.:1110.6
Max. :11.000 Max. :15.000 Max. :176.71 Max. :2784.7
Shape_pattern Control_stimulus
circle :54 bh : 1
diamond : 5 bhv : 1
eyespot :76 bv : 1
lectangle:14 bvv : 1
others : 4 feces : 3
no pattern:146
Note_stimulus
eyespots-defensive posture vs. no eyespots-defensive posture ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 12
single, paper models of the dingy bush brown butterfly; model which has reduced wings and eyespot diameter of approximately 6_mm. A mirror image of the butterfly was created, and a band (approx. 6_mm in length and 5_mm in width) with the same colour as the butterfly's body was added between the two images connecting the mid-section of the body. The butterfly images were then printed in colour on normal paper using a colour laser printer. The paper butterflies were cut out and dipped in paraffin wax to render them waterproof. : 9
solid-eyespots vs. solid-no eyespots ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 9
: 8
countershaded-eyespots vs. countershaded-no eyespots ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 8
models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 7
(Other) :100
Type_prey Shape_prey Diet_bird Bird_sex
artificial:116 abstract_butterfly :64 Invertebrate: 2 NA's:153
real : 37 abstract_caterpillar:52 omnivore : 8
butterfly :37 NA's :143
Bird_age Tn Cn T_mean
nestling: 1 Min. : 7.708 Min. : 7.708 Min. :0.1148
NA's :152 1st Qu.: 20.000 1st Qu.: 20.000 1st Qu.:0.4656
Median : 60.000 Median : 60.000 Median :0.7374
Mean : 63.020 Mean : 63.026 Mean :1.0794
3rd Qu.: 96.000 3rd Qu.: 96.000 3rd Qu.:1.2864
Max. :160.000 Max. :160.000 Max. :6.1300
NA's :134
C_mean MT_mean MC_mean T_sd
Min. :0.1552 Min. :-6.1300 Min. :-4.3900 Min. :0.1403
1st Qu.:0.3357 1st Qu.:-1.2048 1st Qu.:-0.9296 1st Qu.:0.6219
Median :0.4496 Median :-0.5582 Median :-0.3664 Median :0.9192
Mean :0.8256 Mean :-0.6946 Mean :-0.4626 Mean :1.2667
3rd Qu.:1.1137 3rd Qu.:-0.1148 3rd Qu.:-0.1552 3rd Qu.:1.8102
Max. :4.3900 Max. : 0.8822 Max. : 0.9584 Max. :5.4821
NA's :134 NA's :128 NA's :128 NA's :131
C_sd T_proportion C_proportion Study_design
Min. :0.0864 Min. :0.01598 Min. :0.0100 dependent : 1
1st Qu.:0.1422 1st Qu.:0.19510 1st Qu.:0.1100 independent:152
Median :0.2532 Median :0.31679 Median :0.1896
Mean :0.4709 Mean :0.36705 Mean :0.2783
3rd Qu.:0.4555 3rd Qu.:0.49938 3rd Qu.:0.4125
Max. :3.6547 Max. :0.90000 Max. :0.8333
NA's :131 NA's :19 NA's :19
Dataset Mean_median T_mean_median C_mean_median
prey:153 mean : 1 Min. :0.1085 Min. :0.1424
median: 18 1st Qu.:0.4496 1st Qu.:0.3137
NA's :134 Median :0.6934 Median :0.4112
Mean :1.0349 Mean :0.7883
3rd Qu.:1.2320 3rd Qu.:1.0391
Max. :6.1300 Max. :4.3900
NA's :134 NA's :134
Type_of_variance_statistic T_se C_se T_variance_q1
IQR : 18 Min. :0.040 Min. :0.0200 Min. :0.07075
SE : 1 1st Qu.:0.055 1st Qu.:0.0350 1st Qu.:0.28640
NA's:134 Median :0.065 Median :0.0450 Median :0.47294
Mean :0.185 Mean :0.1225 Mean :0.52460
3rd Qu.:0.195 3rd Qu.:0.1325 3rd Qu.:0.72800
Max. :0.570 Max. :0.3800 Max. :1.22170
NA's :149 NA's :149 NA's :135
T_variance_q3 C_variance_q1 C_variance_q3 Note
Min. :0.1651 Min. :0.1136 Min. :0.2096 :146
1st Qu.:0.6584 1st Qu.:0.2594 1st Qu.:0.4316 Big asymmetry 1 : 1
Median :0.9294 Median :0.3159 Median :0.5600 Big asymmetry 2 : 1
Mean :1.1200 Mean :0.4762 Mean :0.8185 Control with spots: 1
3rd Qu.:1.6352 3rd Qu.:0.7712 3rd Qu.:1.3267 Mid asymmetry 1 : 1
Max. :2.3216 Max. :0.9481 Max. :1.6880 Mid asymmetry 2 : 1
NA's :135 NA's :135 NA's :135 (Other) : 2
lnRR lnRR_var Obs_ID Log_diameter
Min. :-0.81549 Min. :0.002201 Min. : 1 Min. :0.5306
1st Qu.:-0.01671 1st Qu.:0.011480 1st Qu.: 39 1st Qu.:1.5041
Median : 0.21564 Median :0.022422 Median : 77 Median :1.7918
Mean : 0.24895 Mean :0.058391 Mean : 77 Mean :1.8249
3rd Qu.: 0.46508 3rd Qu.:0.047242 3rd Qu.:115 3rd Qu.:2.1258
Max. : 2.24770 Max. :0.434523 Max. :153 Max. :2.7081
Log_area Log_background
Min. :0.8197 Min. :4.864
1st Qu.:2.7666 1st Qu.:6.438
Median :3.3420 Median :6.818
Mean :3.2987 Mean :6.673
3rd Qu.:3.7614 3rd Qu.:7.013
Max. :5.1745 Max. :7.932
Code
summary(dt_all)
Study_ID Cohort_ID Shared_control_ID Year
Brilot_2009 : 40 Jones_1980_1 : 16 Jones_1980_a : 16 Min. :1957
Hossie_2013 : 25 Hossie_2013_13: 13 Hossie_2013_g: 13 1st Qu.:2009
Hossie_2012 : 24 Brilot_2009_1 : 10 Brilot_2009_a: 10 Median :2010
Stevens_2007: 20 Brilot_2009_2 : 10 Brilot_2009_b: 10 Mean :2009
Ho_2016 : 18 Brilot_2009_3 : 10 Brilot_2009_c: 10 3rd Qu.:2013
Jones_1980 : 16 Brilot_2009_4 : 10 Brilot_2009_d: 10 Max. :2022
(Other) :127 (Other) :201 (Other) :201
Country Data_source Data_location
UK :138 fig. 3 : 33 supplementary Material: 54
Canada : 57 fig. 4 : 32 p.187 : 24
Sweden : 32 fig. S2 : 30 p.186 : 16
Singapore: 18 table. 1 : 23 p.214 : 16
Finland : 16 fig. 2 : 19 p.387 : 12
US : 5 table. S1: 18 p.1223 : 10
(Other) : 4 (Other) :115 (Other) :138
Bird_species Bird_common_name Prey_species
none :143 none :143 none :204
Gallus_gallus : 48 domestic fowl : 48 Mycalesis_perseus: 18
Sturnus_vulgaris : 42 common starling: 42 Saturnia_pavonia : 13
Parus_caeruleus : 27 blue tit : 27 Lasiommata_megera: 11
Ficedula_hypoleuca: 4 pied flycatcher: 4 Inachis_io : 8
Parus_major : 3 great tit : 3 Thyatira batis : 7
(Other) : 3 (Other) : 3 (Other) : 9
Prey_common_name Response Measure
none :204 continuous : 94 latency : 61
dingy bush brown butterfly: 18 proportion1:147 number : 34
emperor moth : 13 proportion2: 29 proportion:173
wall brown butterfly : 11 time : 2
peacock butterfly : 8
Thyatira batis : 7
(Other) : 9
Direction Detail_result
Decrease: 30 survival :127
Increase:209 number of attacked : 19
Neutral : 31 latency to attack : 10
proportion of time spent near eyespot: 9
latency to approach the food bowl : 8
latency to first movement : 8
(Other) : 89
Note_result
:231
calculated by AM; (total-predated)/total : 24
the time from landing on the perch in front of the butterfly until the attack was launched : 4
mean time in seconds from the beginning of a trial to when a blue tit first visited the log on the floor (first visit): 3
AM culculated the survival rate from raw data : 2
2 cm length : 1
(Other) : 5
Treatment_stimulus Number_pattern Diameter_pattern Area_pattern
conspicuous: 84 Min. : 1.000 Min. : 1.70 Min. : 2.27
eyespot :186 1st Qu.: 2.000 1st Qu.: 4.50 1st Qu.: 15.90
Median : 2.000 Median : 7.00 Median : 38.48
Mean : 2.293 Mean :10.46 Mean :130.34
3rd Qu.: 2.000 3rd Qu.:11.48 3rd Qu.: 79.64
Max. :11.000 Max. :31.28 Max. :490.87
Area_background Shape_pattern Control_stimulus
Min. : 129.6 circle : 60 bh : 1
1st Qu.: 770.0 diamond : 5 bhv : 1
Median : 1040.0 eyespot :186 bv : 1
Mean : 3040.4 lectangle: 14 bvv : 1
3rd Qu.: 1444.0 others : 4 camouflage: 10
Max. :26400.0 stripe : 1 feces : 3
no pattern:253
Note_stimulus
: 30
eyespots-defensive posture vs. no eyespots-defensive posture ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 12
single, paper models of the dingy bush brown butterfly; model which has reduced wings and eyespot diameter of approximately 6_mm. A mirror image of the butterfly was created, and a band (approx. 6_mm in length and 5_mm in width) with the same colour as the butterfly's body was added between the two images connecting the mid-section of the body. The butterfly images were then printed in colour on normal paper using a colour laser printer. The paper butterflies were cut out and dipped in paraffin wax to render them waterproof. : 9
solid-eyespots vs. solid-no eyespots ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 9
countershaded-eyespots vs. countershaded-no eyespots ;models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 8
models were based loosely on the late instars of Papilio canadensis and Papilio glaucus caterpillars : 7
(Other) :195
Type_prey Shape_prey Diet_bird Bird_sex
artificial:204 abstract_butterfly :78 grainivore : 1 both : 50
real : 66 abstract_caterpillar:68 Invertebrate: 4 female: 12
abstract_prey :58 omnivore :122 male : 16
butterfly :66 NA's :143 NA's :192
Bird_age Tn Cn T_mean
adult : 48 Min. : 4.00 Min. : 4.0 Min. : 0.0004
chick : 38 1st Qu.: 8.25 1st Qu.: 9.0 1st Qu.: 0.6021
juvenile: 4 Median : 20.00 Median : 20.0 Median : 7.2595
nestling: 1 Mean : 42.09 Mean : 41.9 Mean : 100.4589
NA's :179 3rd Qu.: 80.00 3rd Qu.: 80.0 3rd Qu.: 93.1250
Max. :160.00 Max. :160.0 Max. :1180.4878
NA's :150
C_mean MT_mean MC_mean
Min. : 0.0400 Min. :-556.1000 Min. :-2115.0000
1st Qu.: 0.3675 1st Qu.: -1.3776 1st Qu.: -1.1749
Median : 3.9950 Median : -0.1148 Median : -0.1552
Mean : 92.8595 Mean : -26.1327 Mean : -72.1179
3rd Qu.: 56.6866 3rd Qu.: 0.8822 3rd Qu.: 0.8949
Max. :2115.0000 Max. : 0.9996 Max. : 0.9584
NA's :150 NA's :209 NA's :209
T_sd C_sd T_proportion C_proportion
Min. : 0.0100 Min. : 0.050 Min. :0.0100 Min. :0.0100
1st Qu.: 0.5278 1st Qu.: 0.229 1st Qu.:0.1715 1st Qu.:0.1046
Median : 4.2319 Median : 2.711 Median :0.3152 Median :0.2027
Mean : 67.7837 Mean : 64.351 Mean :0.3531 Mean :0.2831
3rd Qu.: 59.4457 3rd Qu.: 52.998 3rd Qu.:0.5000 3rd Qu.:0.4396
Max. :731.8482 Max. :1052.175 Max. :0.9000 Max. :0.8333
NA's :147 NA's :147 NA's :94 NA's :94
Study_design Dataset Mean_median T_mean_median
dependent : 65 predator:117 mea : 1 Min. : 0.0004
independent:205 prey :153 mean :100 1st Qu.: 0.6584
median: 19 Median : 7.2766
NA's :150 Mean : 89.8277
3rd Qu.: 58.0122
Max. :1180.4878
NA's :134
C_mean_median Type_of_variance_statistic T_se
Min. : 0.0000 IQR : 19 Min. : 0.00000
1st Qu.: 0.4022 SD : 3 1st Qu.: 0.08208
Median : 4.7365 SE : 29 Median : 3.52000
Mean : 83.4133 SE : 1 Mean : 24.82370
3rd Qu.: 46.5061 SEM : 68 3rd Qu.: 24.55107
Max. :2115.0000 NA's:150 Max. :182.92683
NA's :134 NA's :169
C_se T_variance_q1 T_variance_q3 C_variance_q1
Min. : 0.0000 Min. : 0.07075 Min. : 0.1651 Min. : 0.1136
1st Qu.: 0.0877 1st Qu.: 0.28640 1st Qu.: 0.6656 1st Qu.: 0.2594
Median : 1.1000 Median : 0.50720 Median : 0.9296 Median : 0.3440
Mean : 25.6820 Mean : 4.57594 Mean : 14.0085 Mean : 1.9774
3rd Qu.: 19.8747 3rd Qu.: 0.78560 3rd Qu.: 1.7799 3rd Qu.: 0.8048
Max. :372.0000 Max. :77.50000 Max. :246.0000 Max. :29.0000
NA's :169 NA's :251 NA's :251 NA's :251
C_variance_q3
Min. : 0.2096
1st Qu.: 0.4340
Median : 0.5936
Mean : 2.6702
3rd Qu.: 1.4151
Max. :36.0000
NA's :251
Note
:218
authors only reported total sample size (left eyespots and right eyespots), so the sample size was equally divided between the two stimuli: 8
Mann-Whitney U test; p < 0.002 : 4
ア 1 SEM : 4
Calculated by AM : 3
(Other) : 31
NA's : 2
lnRR lnRR_var Obs_ID Log_diameter
Min. :-2.15769 Min. :0.0008295 Min. : 1.00 Min. :0.5306
1st Qu.:-0.03772 1st Qu.:0.0111211 1st Qu.: 68.25 1st Qu.:1.5041
Median : 0.14784 Median :0.0234099 Median :135.50 Median :1.9459
Mean : 0.26023 Mean :0.0872373 Mean :135.50 Mean :2.0819
3rd Qu.: 0.47455 3rd Qu.:0.0732753 3rd Qu.:202.75 3rd Qu.:2.4407
Max. : 4.16777 Max. :1.3885984 Max. :270.00 Max. :3.4430
Log_area Log_background
Min. :0.8197 Min. : 4.864
1st Qu.:2.7666 1st Qu.: 6.646
Median :3.6503 Median : 6.947
Mean :3.8513 Mean : 7.170
3rd Qu.:4.3774 3rd Qu.: 7.275
Max. :6.1962 Max. :10.181
I cannot attach the caption to datatable() format table. I need to use kable() format table?
Code
datatable(dt_all, caption ="Dataset for meta-analysis", options =list(pageLength =10, scrollX =TRUE))
Table 2 - Dataset for meta-analysis
If phylogeny do not explain heterogeniety much, we will not need to consider it and the two datasets can be merged.
We used meta-analytical models to calculate total I2 (a measure of heterogeneity not caused by sampling error; Higgins. et al., 2003) and the partial I2 explained by each random factor.
Based on this, we need not to consider phylogenetic relatedness from our meta-regressions as this random factor did not explain much of the heterogeneity between effect sizes (partial I2 < 0.001%), then we can combine two datasets (predator and prey) for meta-analysis.
Code
phy_model <-function(cor_tree = vcv_tree){ model <-rma.mv(yi = lnRR,V = VCV_pred,random =list(~1| Study_ID,~1| Shared_control_ID,~1| Cohort_ID,~1| Obs_ID,~1| Bird_species,~1| Phylogeny),R =list(Phylogeny = cor_tree),test ="t",method ="REML",sparse =TRUE,data = dat_pred) model}tree_50 <- trees[1:50]vcv_tree_50 <-map(tree_50, ~vcv(.x, corr =TRUE))# Run multiple meta-analyses with 50 different trees and obtain the combined resultma_50 <-mclapply(vcv_tree_50, phy_model, mc.cores =8)
Code
ma_50 <-readRDS(here("Rdata", "ma_50.RDS"))# combining the resultsest_50 <-map_dbl(ma_50, ~ .x$b[[1]])se_50 <-map_dbl(ma_50, ~ .x$se)df_50 <-c(rbind(est_50, se_50))# creating an array required by pool.mimy_array <-array(df_50, dim =c(1, 2, 50))com_res <-round(pool.mi(my_array), 4)
Code
knitr::kable(com_res, caption ="Combined result of 50 phylogenetic trees")
We used meta-analytical models to calculate total I2 (a measure of heterogeneity not caused by sampling error; Higgins. et al., 2003) and the partial I2 explained by each random factor.
Our dataset includes 4 types of prey type: real butterfly, abstract butterfly, abstract caterpillar, and abstract prey. Is there significant difference of effect size between two stimuli?
orchard_plot(pred_mr_prey_shape,mod ="Shape_prey",group ="Study_ID",xlab ="Shape of prey",angle =45) +scale_colour_okabe_ito(order =6:9)+scale_fill_okabe_ito(order =6:9)
Figure 4— Effect size and prey shape
2.2 Correlation visualisation and choose moderators for multi-moderator meta-regression in predator dataset
Before we run multi-moderator meta-regressions, we need to consider the correlation between moderators. Area, diameter and background seem to be correlated. We visualised the correlation between these variables.
Figure 6— Correlation between categorical variables
We should not include “Shape_prey” and “Type_prey” in the model at the same time. Because they are correlated.
We used model R2 values to find better model and modelator VIF values to check multicollinearity between moderators. Higher R2 indicates better model and VIF > 2 indicates multicollinearity.
# these figs were created by multi meta-regression model results# log-transformed areapred_p4 <-bubble_plot(pred_mr_area,mod ="Log_area",group ="Study_ID",xlab ="Log-transformed area") +scale_x_continuous(breaks =seq(0,7,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# number of patternspred_p5 <-bubble_plot(pred_mr_num,mod ="Number_pattern",group ="Study_ID",xlab ="Number of patterns") +scale_x_continuous(breaks =seq(0,11,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# combinepred_p4 / pred_p5 +plot_annotation(tag_levels ="a")# output figure as pdf# ggsave("fig2_multi.pdf", width = 10, height = 10, dpi = 450)
Figure 14— Continuous moderators
Code
# funnel plot# pdf("fig3.pdf")funnel(ma_pred, yaxis ="seinv", xlab ="Standarised residuals",ylab ="Precision (inverse of SE)",xlim =c(-4.0, 4.5), ylim =c(0.01, 80.0), col =c(alpha("mediumvioletred", 0.5)),cex =0.7)# dev.off()# Egger's test and decline effectpred_p7 <-bubble_plot(pred_bias_model,mod ="sqrt_inv_e_n",group ="Study_ID",xlab ="Square root of inverse of effective sample size") +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5)) pred_p8 <-bubble_plot(pred_year_model,mod ="Year",group ="Study_ID",xlab ="Year of publication") +scale_y_continuous(breaks =seq(-2.5, 4.0, 1.5)) # combine plots created by bubble_plot()pred_pub <- pred_p7 / pred_p8pred_pub +plot_annotation(tag_levels ='a') # output figure as pdf# ggsave("fig4.pdf", width = 10, height = 10, dpi = 450)
Figure 15— Funnel plot
Figure 16— Egger’s test and Decline effect
Figure 17— Publication bias
3 Meta-analysis - prey dataset
We used meta-analytical models to calculate total I2 (a measure of heterogeneity not caused by sampling error; Higgins. et al., 2003) and the partial I2 explained by each random factor.
Our dataset includes 4 types of prey type: real butterfly, abstract butterfly, abstract caterpillar, and abstract prey. Is there significant difference of effect size between two stimuli?
orchard_plot(prey_mr_prey_shape,mod ="Shape_prey",group ="Study_ID",xlab ="Shape of prey",angle =45) +scale_colour_okabe_ito(order =6:9)+scale_fill_okabe_ito(order =6:9)
Figure 20— Effect size and prey shape
3.2 Correlation visualisation and choose moderators for multi-moderator meta-regression in preyator dataset
Before we run multi-moderator meta-regressions, we need to consider the correlation between moderators. Area, diameter and background seem to be correlated. We visualised the correlation between these variables.
Figure 22— Correlation between categorical variables
We should not include “Shape_prey” and “Type_prey” in the model at the same time. Because they are correlated.
We used model R2 values to find better model and modelator VIF values to check multicollinearity between moderators. Higher R2 indicates better model and VIF > 2 indicates multicollinearity.
# these figs were created by multi meta-regression model results# log-transformed areaprey_p4 <-bubble_plot(prey_mr_area,mod ="Log_area",group ="Study_ID",xlab ="Log-transformed area") +scale_x_continuous(breaks =seq(0,7,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# number of patternsprey_p5 <-bubble_plot(prey_mr_num,mod ="Number_pattern",group ="Study_ID",xlab ="Number of patterns") +scale_x_continuous(breaks =seq(0,11,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# combineprey_p4 / prey_p5 +plot_annotation(tag_levels ="a")# output figure as pdf# ggsave("fig2_multi.pdf", width = 10, height = 10, dpi = 450)
Figure 30— Continuous moderators
3.6.3 Publication bias
Code
# funnel plot# pdf("fig3.pdf")funnel(ma_prey, yaxis ="seinv", xlab ="Standarised residuals",ylab ="Precision (inverse of SE)",xlim =c(-4.0, 4.5), ylim =c(0.01, 80.0), col =c(alpha("mediumvioletred", 0.5)),cex =0.7)# dev.off()# Egger's test and decline effectprey_p7 <-bubble_plot(prey_bias_model,mod ="sqrt_inv_e_n",group ="Study_ID",xlab ="Square root of inverse of effective sample size") +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5)) prey_p8 <-bubble_plot(prey_year_model,mod ="Year",group ="Study_ID",xlab ="Year of publication") +scale_y_continuous(breaks =seq(-2.5, 4.0, 1.5)) # combine plots created by bubble_plot()prey_pub <- prey_p7 / prey_p8prey_pub +plot_annotation(tag_levels ='a') # output figure as pdf# ggsave("fig4.pdf", width = 10, height = 10, dpi = 450)
(a) Funnel plot
(b) Egger’s test and Decline effect
Figure 31— Publication bias
4 Meta-analysis - all dataset
We used meta-analytical models to calculate total I2 (a measure of heterogeneity not caused by sampling error; Higgins. et al., 2003) and the partial I2 explained by each random factor.
Which random effects remove in our models?
We can remove Shared control ID and Cohort ID
Code
# I exclude cohort_ID because sigma^2.2 = 0 and I2 = 0ma_all <-rma.mv(yi = lnRR,V = VCV, random =list(~1| Study_ID,~1| Shared_control_ID,~1| Cohort_ID,~1| Obs_ID),test ="t",method ="REML", sparse =TRUE,data = dt_all)summary(ma_all)
Our dataset includes 4 types of prey type: real butterfly, abstract butterfly, abstract caterpillar, and abstract prey. Is there significant difference of effect size between two stimuli?
mat_ex <-cbind(contrMat(rep(1,length(mr_prey_shape$ci.ub)),type ="Tukey"))sig_test <-summary(glht(mr_prey_shape, linfct= mat_ex), test =adjusted("none"))sig_test
Simultaneous Tests for General Linear Hypotheses
Fit: rma.mv(yi = lnRR, V = VCV, mods = ~Shape_prey - 1, random = list(~1 |
Study_ID, ~1 | Obs_ID), data = dt_all, method = "REML", test = "t",
sparse = TRUE)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
2 - 1 == 0 -0.25583 0.16444 -1.556 0.120
3 - 1 == 0 -0.31057 0.21242 -1.462 0.144
4 - 1 == 0 -0.09561 0.14577 -0.656 0.512
3 - 2 == 0 -0.05474 0.22317 -0.245 0.806
4 - 2 == 0 0.16022 0.16104 0.995 0.320
4 - 3 == 0 0.21496 0.20980 1.025 0.306
(Adjusted p values reported -- none method)
R2_marginal
R2_conditional
0.0521
0.2312
Table XX. Model goodness-of-fit
Code
orchard_plot(mr_prey_shape,mod ="Shape_prey",group ="Study_ID",xlab ="Shape of prey",angle =45) +scale_colour_okabe_ito(order =6:9)+scale_fill_okabe_ito(order =6:9)
Figure 35— Effect size and prey shape
4.2 Correlation visualisation and choose moderators
Before we run multi-moderator meta-regressions, we need to consider the correlation between moderators. Area, diameter and background seem to be correlated. We visualised the correlation between these variables.
Figure 37— Correlation between categorical variables
We should not include “Shape_prey” and “Type_prey” in the model at the same time. Because they are correlated.
We used model R2 values to find better model and modelator VIF values to check multicollinearity between moderators. Higher R2 indicates better model and VIF > 2 indicates multicollinearity.
# these figs were created by multi meta-regression model results# log-transformed areap4 <-bubble_plot(mr_area,mod ="Log_area",group ="Study_ID",xlab ="Log-transformed area") +scale_x_continuous(breaks =seq(0,7,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# number of patternsp5 <-bubble_plot(mr_num,mod ="Number_pattern",group ="Study_ID",xlab ="Number of patterns") +scale_x_continuous(breaks =seq(0,11,1.5)) +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5))# combinep4 / p5 +plot_annotation(tag_levels ="a")# output figure as pdfggsave("fig2_multi.pdf", dpi =450, units ="mm")
Figure 45— Continuous moderators
Code
# funnel plot# pdf("fig3.pdf")funnel(ma_all, yaxis ="seinv", xlab ="Standarised residuals",ylab ="Precision (inverse of SE)",xlim =c(-4.0, 4.5), ylim =c(0.01, 80.0), col =c(alpha("mediumvioletred", 0.5)),cex =0.7)# dev.off()# Egger's test and decline effectp7 <-bubble_plot(bias_model,mod ="sqrt_inv_e_n",group ="Study_ID",xlab ="Square root of inverse of effective sample size") +scale_y_continuous(breaks =seq(-2.5, 4.5, 1.5)) p8 <-bubble_plot(year_model,mod ="Year",group ="Study_ID",xlab ="Year of publication") +scale_y_continuous(breaks =seq(-2.5, 4.0, 1.5)) # combine plots created by bubble_plot()pub <- p7 / p8pub +plot_annotation(tag_levels ='a') # output figure as pdf# ggsave("fig4.pdf", width = 10, height = 10, dpi = 450)